It is well known in the fields of Geology and Earth Science to use tilt sensors to measure the paths of boreholes. Typically, a tilt sensor is a tubular form containing electrolytic, resistive, capacitive, ‘zero-displacement’, or micromachined silicon gravity sensors arranged to sense two degrees of freedom (DOFs) of tilt relative to the gravity field. Normally the two DOFs are orthogonal, and are termed x and y components of tilt. The tilt sensor may be lowered into a borehole and tilt data taken at intervals. Or, several tilt sensors may be arranged one above the other in the borehole and used to detect changes in tilt at known locations. It is also known to use accelerometers lowered into boreholes to measure earthquake vibrations, including s-waves and p-waves. S-waves produce accelerations predominantly parallel to the Earth's surface. It is also known to use magnetic sensors to determine the orientation of sensors in the Earth's magnetic field, including sensors in boreholes.
In addition to boreholes, the above methods are applied to structures such as bridges and buildings, mineshafts, and sensors attached to or buried in the earth or earthworks.
A deficiency of the above tilt sensor methods is the inability to provide continuous real-time measurement and/or to track dynamic shapes. Most of the current tilt sensor technologies do not measure dynamic acceleration such as s-waves during an earthquake. A further deficiency is the lack of a calibrated, deformable, portable substrate to hold the sensors and protect them from water and mechanical forces. A further deficiency is the requirement for a larger number of sensors because the tilt sensors are not arranged within a calibrated structure or a twist-free structure, so that magnetic measurement of orientation about the gravity vector is required.
It is also known to use bend-sensing and bend-and-twist-sensing arrays to measure the dynamic and static shapes of boreholes, buildings, persons, instruments, and geological structures. Examples include Danisch, L. A., Fiber optic bending and position sensor including a light emission surface formed on a portion of a light guide, U.S. Pat. No. 5,321,257, Jun. 14, 1994; Danisch, L. A., Fiber optic bending and position sensor with selected curved light emission surfaces, U.S. Pat. No. 5,633,494, May 27, 1997, Danisch, L. A., Fiber optic bending and position sensor, European Patent No. EP 0 702 780, Oct. 22, 1997, Danisch, L. A., Topological and motion measuring tool, U.S. Pat. No. 6,127,672, Oct. 3, 2000, and Danisch, L. A., Topological and motion measuring tool, U.S. Pat. No. 6,563,107.
In Danisch '672, a 2 DOF bend-sensing array is described that can be used to map a path in 3D. By adding twist as a third DOF (see Danisch, L. A., '107) the sensors in the array can rotate at joints or continuously along the long axis. Danisch, L. A. '107 describes surface-mapping arrays using curvature sensors to measure angles between elements of the surfaces. These sensor arrays use curvature sensors to measure angles along deformable surfaces. Often the sensors are modified optical fibers. A deficiency of 2 DOF bend-sensing arrays or 3 DOF bend-twist-sensing arrays in their most common form is their inability to measure accurately the small angles encountered in many applications including borehole measurements. Although they can resolve small angles over a short time period, drift causes inaccuracies that are a problem for long-term measurements. Inaccuracy may be surmounted by using 2 DOF and 3 DOF couplings between stiff members, and measuring the DOFs of the couplings with highly accurate encoders. However, this leads to great cost and complexity that makes it unlikely they would be used for long-term measurement of deformations.
In Danisch '672 and Danisch '107 surfaces are measured relative to a reference surface in 6 DOF by knowing the angular relationships between elements of the surfaces. The absolute angles of the elements in the ‘World Coordinate System’ (WCS) are not measured directly. They are calculated by integrating the angular relationships, or ‘local’ angles between elements, which are measured by bend sensors. For instance, rods connected by hinges that are all bent in the same vertical plane might have local hinge angles of 10, 20, −10, and 30 degrees. Relative to a reference rod that is horizontal in the World Coordinate System, the WCS angles between the rods are 10, 30, 20, and 50 degrees, obtained by integrating (adding) the local angles along the path. If the lengths of the rods are known and their WCS angles have been determined then the path of the rod system is completely determined.
When the connections between the rods allow for additional DOFs, such as multiaxial bend and twist, then there are 2 or 3 angular DOFs between the rods and the integration requires 3D mathematics. 3D space curve mathematics can be used and are described in Danisch '672 and Danisch '107. Deformable surfaces or volumes, not just collections of rods, may be measured in this way if the angular interrelationships are measurable and the locations of the sensors on the surfaces are known. The measurements are subject to significant errors for all portions of the surface calculated beyond the location of any angular error. Further, drift in the sensors can lead to inaccuracies in shape that must be corrected by putting the surfaces back into a previously captured pose and removing offsets to restore the measured shape to that of the captured pose. However, the measurements are useful because they may be performed with very thin arrays of optical fibers and at very high speed, such as 10,000 frames per second or more for rapidly changing shapes.
For static shapes it is possible to use accelerometers with a frequency response that extends to a constant or ‘DC’ acceleration, so that outputs are responsive to the gravity field, which has a constant acceleration of approximately 9.8 m/s/s. Accurate, low cost, miniature devices made by micromachining silicon (MEMs or MicroMachined ElectroMechanical Sensors) are available in single and dual axis forms. An example is the Analog Devices Inc. ADXL311 integrated circuit which has a response to acceleration from DC to thousands of Hertz (Hz). Dual-axis MEMs devices can resolve sub-degree tilts and maintain high accuracy over many years and a wide temperature range. If an array of these is placed on a deformable surface, an array of tilt signals can be generated that represents the WCS angles of the attachment locations. If the distances between locations are known, the path, surface, or volume shape can be determined to high accuracy. Unlike shape measurements based on integration of local angles, shape measurements based on directly-measured WCS angles are not subject to accumulating errors and can be much more accurate. Alternatives to MEMs sensors include electrolytic tilt sensors, capacitive tilt sensors, inductive tilt sensors, and zero-displacement accelerometers that keep a mass centered in a measuring frame and determine the forces necessary to do so. However, the disadvantage of all prior-art tilt-sensing arrays is that measurements must be made while the shapes are unchanging.
If an array is formed of MEMs acceleration sensors with a wide range of frequency response, the sensors will respond to static acceleration fields like gravity and also to rapidly-changing fields like earthquake vibration. The electronics and software may be arranged to provide output data that represent a long-term average of the total signal (slow data), and other output data that represent only the rapidly-changing components (fast data). The slow data represent the response to gravity and the fast data represent the response to vibration or other rapid movement of the array within the gravity field. The slow data are obtained by averaging many frames of data and otherwise excluding rapidly-changing signals using standard filtering techniques. The fast data are obtained by subtracting the slow data from unfiltered total data. This prior-art technique of obtaining slow and fast data is well-known. If the fast data integrates to zero over time in the filter, then accurate slow data representing the mean shape are obtained. If the mean shape is unchanging, or changing only very slowly, then the fast data represents the vibration present at each sensor within the array. Thus, the array may be used to obtain a static shape from WCS tilt angles (slow data) while the fast data are used to define the vibration applied to the array at each sensor.